Archdiocese of Washington Catholic Schools
Academic Standards
Mathematics
1st GRADE
Standard 1 - Number Sense
Students understand symbols, objects, and pictures used to represent numbers up to 100 and show an
understanding of fractions.
1.1.1
Count, read, and write whole numbers* up to 100.
Example: Write 72 for the number “seventy-two.”
1.1.2
Count and group objects in ones and tens.
Example: Separate a group of 34 blocks into three groups of 10 blocks and 4 single blocks.
1.1.3
Identify the number of tens and ones less than 100.
Example: How many tens and how many ones are in 56? Explain your answer.
1.1.4
Name the number that is one more than or one less than any number up to 100.
Example: Name the number one less than 78.
1.1.5
Compare whole numbers up to 10 and arrange them in numerical order.
Example: Arrange the numbers 5, 2, and 9 in order from greatest to least.
1.1.6
Match the number names first, second, third, etc. with an ordered set of up to 10 items.
Example: Point out the fifth child from the front of a line of children.
1.1.7
Recognize when a shape is divided into congruent (matching) parts.
Example: Given a rectangle with lines dividing it into parts, decide whether the parts are the
same size.
1.1.8
For a shape divided into 8 or fewer congruent (matching) parts, describe a shaded portion as “__out of
__ parts” and write the fraction.
Example: Given a circle divided into 4 equal parts with 3 of the parts shaded, describe the
shaded portion of “3 out of 4 parts” and write the fraction for the shaded portion.
1.1.9
For a set of 8 or fewer objects, describe a subset as “__out of __ parts” and write the fraction.
Example: Given 3 red pencils and 2 blue pencils, describe the subset of red pencils as “3 out of
5 parts” and write the fraction of the pencils that are red.
1.1.10 Represent, compare, and interpret data using pictures and picture graphs.
Example: Use a picture graph to show how many dogs, cats, etc. your friends have. Which kind
of pet appears most often? Explain you answer.
*whole numbers: 0, 1, 2, 3, etc.
Grade 1
Mathematics
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Archdiocese of Washington Catholic Schools
Academic Standards
Mathematics
Standard 2 – Computation
Students demonstrate the meaning of addition and subtraction and use these operations to solve problems.
1.2.1
Show the meaning of addition (putting together, increasing) using objects.
Example: Put together 3 pencils and 5 pencils. Tell how many pencils you have and explain
what you are doing.
1.2.2
Show the meaning of subtraction (taking away, comparing, finding the difference) using objects.
Example: Take away 6 blocks from a group of 10. Tell how many blocks are left and explain
what you are doing.
1.2.3
Show equivalent forms of the same number (up to 20) using objects, diagrams, and numbers.
Example: Write 15 as 8 + 7, 5 + 5 + 5, 10 + 5, 15 + 0, 17 – 2, etc.
1.2.4
Demonstrate mastery of the addition facts (for totals up to 20) and the corresponding subtraction facts.
Example: Add 11 + 8, subtract 16 – 9, add 4 + 7.
1.2.5
Understand the meaning of the symbols +, -, and =.
Example: Use symbols to write the number sentence “one added to three equals four.”
1.2.6
Understand the role of zero in addition and subtraction.
Example: You start with 6 eggs and then give away 6 eggs. How many eggs do you have now?
1.2.7
Understand and use the inverse relationship between addition and subtraction facts (such as 4 + 2 = 6,
6 – 2 = 4, etc.) to solve simple problems.
Example: List three other facts using addition or subtraction that are related to 3 + 5 = 8.
Grade 1
Mathematics
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Archdiocese of Washington Catholic Schools
Academic Standards
Mathematics
Standard 3 – Algebra and Functions
Students use number sentences with the symbols +, -, and = to solve problems.
1.3.1
Write and solve number sentences from problem situations involving addition and subtraction.
Example: You have 3 pencils and your friend has 2 pencils. You want to know how many
pencils you have altogether. Write a number sentence for this problem and use it to find the total
number of pencils.
1.3.2
Create word problems that match given number sentences involving addition and subtraction.
Example: Tell a story or draw a picture for a problem that can be solved using the number
sentence 3 + 6 = 9.
1.3.3
Recognize and use the relationship between addition and subtraction.
Example: Start with 8 blocks. Add 5 more blocks. How many do you have? Now take away 5
blocks. How many do you have now? Explain your answer.
1.3.4
Create and extend number patterns using addition.
Example: A number pattern begins with these numbers 1, 3, 5, … Tell what the next number will
be and explain how you decided on that number.
Grade 1
Mathematics
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Archdiocese of Washington Catholic Schools
Academic Standards
Mathematics
Standard 4 – Geometry
Students identify common geometric shapes, classify them by common attributes, and describe their relative
position or their location in space.
1.4.1
Identify, describe, compare, sort, and draw triangles, rectangles, squares, and circles.
Example: Draw a square and a circle and write their names next to them.
1.4.2
Identify triangles, rectangles, squares, and circles as the faces* of three-dimensional objects.
Example: Look at a collection of solid objects and find triangles and squares on their sides.
1.4.3
Classify and sort familiar plane and solid objects by position, shape, size, roundness, and other
attributes. Explain the rule you used.
Example: Group a collection of objects by something they have in common. Explain your
grouping.
1.4.4
Identify objects as two- or three-dimensional.
Example: Sort various objects (cube, square, triangle, prism) into the categories “twodimensional” and “three-dimensional.” Explain your choices.
1.4.5
Give and follow directions for find a place or object.
Example: Show someone how to get to the school library by making a map or diagram.
1.4.6
Arrange and describe objects in space by position and direction: near, far, under, over, up, down,
behind, in front of, next to, to the left or right of.
Example: Name objects that are near your desk and objects that are in front of it. Explain why
there may be some objects in both groups.
1.4.7
Identify geometric shapes and structures in the environment and specify their location.
Example: Find as many rectangles as you can in your classroom. Record the rectangles that
you found by making drawings or using a camera.
*face: flat side
Grade 1
Mathematics
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Archdiocese of Washington Catholic Schools
Academic Standards
Mathematics
Standard 5 – Measurement
Students learn how to measure length, as well as how to compare, order, and describe other kinds of
measurement.
1.5.1
Measure the length of objects by repeating a non-standard unit or a standard unit.
Example: Measure the length of your desk in pencil-lengths.
1.5.2
Use different units to measure the length of the same object and predict whether the measure will be
greater or smaller when a different unit is used.
Example: If you measure your desk with a shorter pencil, will the number of pencil-lengths be
more or less? Measure the desk to find out your answer.
1.5.3
Recognize the need for a fixed unit of length.
Example: Give students different lengths of string and have them measure the width of a
doorway. Talk about why their answers are different and the kinds of problems this can cause.
1.5.4
Measure and estimate the length of an object to the nearest inch and centimeter.
Example: Have some students measure the width of the doorway in inches and some measure
it in centimeters. Discuss why these are better ways of measuring than using the pieces of
string.
1.5.5
Compare and order objects according to area, capacity, weight, and temperature, using direct
comparison or a non-standard unit.
Example: Use a scale or balance to see how many crayons weigh the same as a shoe.
1.5.6
Tell time to the nearest half-hour and relate time events (before/after, shorter/longer).
Example: Is recess before or after lunch?
1.5.7
Identify and give the values of pennies, nickels, and dimes.
Example: How many pennies have the same value as two nickels?
Grade 1
Mathematics
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Archdiocese of Washington Catholic Schools
Academic Standards
Mathematics
Standard 6 – Problem Solving
Students make decisions about how to set up a problem.
1.6.1
Choose the approach, materials, and strategies to use in solving problems.
Example: Solve the problem: “The number 10 can be written in different ways using addition: 10
= 4 + 6 or 10 = 1 + 9 … Find how many ways you can write 10 by adding two numbers.” Use
blocks to set up the problem.
1.6.2
Use tools such as objects or drawings to model problems.
Example: In the first example, show the number 10 using addition of whole numbers by counting
out ten blocks. Divide them into two piles and write a number sentence that shows the number
in each pile of blocks.
Students solve problems and justify their reasoning.
1.6.3
Explain the reasoning used and justify the procedures selected in solving a problem.
Example: In the first example, make two piles of ten blocks; separate one block from the first
pile and count the number of blocks left. Separate two blocks from the second pile and count
the number left. Describe any patter of numbers that you find.
1.6.4
Make precise calculations and check the validity of the results in the context of the problem.
Example: In the first example, check your results by setting out 10 blocks showing 1 + 9,
another 10 blocks showing 2 + 8, and so on. Continue to count out piles of 10 blocks to find the
total number of ways that ten blocks can be separated into two piles. Describe the patterns that
you find and how you find that you have found all of them.
1.6.5
Understand and use connections between two problems.
Example: Use the problem you have just solved to find how many ways you can write 16 by
adding two numbers.
Grade 1
Mathematics
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